Question

Nth term sequences, please may I get some help. 15 p.

Answer 1

Answer:

$(n+2)^2+6$

Step-by-step explanation:

Pattern 1 consists of

$3+3\times 3+3$ small squares (here n = 1 and $3\times 3=(1+2)\times (1+2)$).

Pattern 2 consists of

$3+4\times 4+3$ small squares (here n = 2 and $4\times 4=(2+2)\times (2+2)$).

Pattern 3 consists of

$3+5\times 5+3$ small squares (here n = 3 and $5\times 5=(3+2)\times (3+2)$).

Thus, pattern n consists of

$3+(n+2)\times (n+2)+3=6+(n+2)^2$ small squares.